Thermoelectric DC conductivities and Stokes flows on black hole horizons

Banks, E.; Donos, A.; Gauntlett, J.P.

Abstract

We consider a general class of electrically charged black holes of Einstein-Maxwell-scalar theory that are holographically dual to conformal field theories at finite charge density which break translation invariance explicitly. We examine the linearised perturbations about the solutions that are associated with the thermoelectric DC conductivity. We show that there is a decoupled sector at the black hole horizon which must solve generalised Stokes equations for a charged fluid. By solving these equations we can obtain the DC conductivity of the dual field theory. For Q-lattices and one-dimensional lattices we solve the fluid equations to obtain closed form expressions for the DC conductivity in terms of the solution at the black hole horizon. We also determine the leading order DC conductivity for lattices that can be expanded as a perturbative series about translationally invariant solutions.

Citation

Banks, E., Donos, A., & Gauntlett, J. (2015). Thermoelectric DC conductivities and Stokes flows on black hole horizons. Journal of High Energy Physics, 2015(10), Article 103. https://doi.org/10.1007/jhep10%282015%29103

• Journal Article Type: Article
• Acceptance Date: Sep 16, 2015
• Online Publication Date: Oct 15, 2015
• Publication Date: Oct 15, 2015
• Deposit Date: Jan 2, 2016
• Publicly Available Date: Apr 14, 2016
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2015
• Issue: 10
• Article Number: 103
• DOI: https://doi.org/10.1007/jhep10%282015%29103
• Public URL: https://durham-repository.worktribe.com/output/1393177